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Particle retardation in vertically oscillating fluids
Author(s) -
Houghton Gerald
Publication year - 1968
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450460202
Subject(s) - classical mechanics , mathieu function , physics , particle (ecology) , drag , particle velocity , nonlinear system , mechanics , equations of motion , quantum mechanics , oceanography , geology
Abstract An analytic expression has been deduced for the ultimate velocity of a free particle in a vertically oscillating fluid by evaluating asymptotic forms of Floquet's solution to the Mathieu equation arising from the nonlinear Langevin equation describing the particle‐fluid interactions. Using general Mathieu theory it has been rigorously demonstrated that directional particle motion in a gravitational field can be retarded by sinusoidal fluid oscillations when the particle‐fluid drag law is of square form. The earlier Rayleigh‐Ritz approximation (Houghton 1966) for the retarded particle velocity is shown to be in good agreement with the results of Mathieu theory, as summarized in graphical form.